While reading this paper on describing biological control of movement as a servomechanism, I came across a good explanation of the formation and value for muscle memory (even though the paper did not state it in the exact terms).
The gist of the paper is that, accurate biological movement would require both desired position AND velocity signals from the central nervous system (CNS), forming a proportional-plus-derivative control loop from the musculer-skeletal system and the reflex feedbacks.
There are various ways in which the CNS can generate the positional and the velocity signals need for a certain movement. There’s evidence that the cortex contains representations of the velocity profile of a movement (and thus requiring an integrating circuit for position). The converse is also a possibility.
However, my favorite theory is one that suggests the basis for muscle memory:
A strategy based on learning could also be imagined. The CNS might precompute only the positions for the trajectory of a novel movement. The movement then could be executed via one of the classical equilibrium-point models using a relatively high level of stiffness to ensure the fidelity of the movement. The CNS could then “remember” the signals generated by the velocity signals during these learning trials. For subsequent trials at low stiffness, the CNS would utilize this memory as the required velocity reference signal. A difficulty with any memory-based control scheme is that of initializing the memory for novel movements. The learning scheme based on our control model explicitly addresses this problem. By performing novel movements initially at high stiffness, the sensory organs themselves produce the exact pattern of activation required as a velocity reference signal for subsequent low-gain movements.
This is a pretty old paper (from 1993), so I’m not sure how much more advancements have been made on this theory. Nevertheless, the same principle can be applied to a number of physical and abstract systems.